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Two Encryption Algorithms based on Layered Cellular Automata

Two Encryption Algorithms based on Layered Cellular Automata. Zhang Xing. Content. Cellular Automata LRCA(Layered and Reversible Cellular Automata) TLCA(T-shaped Layered Cellular Automata). Cellular Automata(CA) is dynamic and discrete system.

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Two Encryption Algorithms based on Layered Cellular Automata

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  1. Two Encryption Algorithms based on Layered Cellular Automata Zhang Xing

  2. Content • Cellular Automata • LRCA(Layered and Reversible Cellular Automata) • TLCA(T-shaped Layered Cellular Automata)

  3. Cellular Automata(CA) is dynamic and discrete system • A Cellular Automaton (CA) is an infinite, regular lattice of simple finite state machines that change their states synchronously, according to a local update rule that specifies the new state of each cell based on the old states of its neighbors. • Cellular automata are a collection of cells that each adapts one of a finite number of states. Single cells change in states by following a local rule that depends on the environment of the cell.

  4. CA can be represented by {D,K,N,f,B} • D defines the dimension of CA may be 1D, 2D,… (Figure 2) • K holds set of possible states of all cells in a CA • {1,2,3,…} • {born,death} • {black, white} … • for convenience , {0,1}

  5. CA can be represented by {D,K,N,f,B} • N defines the set of neighborhood states(Figure 3) • 3 neighbour (a) • Von-Neumann(b) • Moore neighborhood(c) • f is transition function ( Transition rule) • B defines the boundary condition • Periodic boundary (Figure 4) • Fixed boundary

  6. inherent properties: Discrteness, Parallelism, Locality, Homogeneity, Unpredictability classification Uniform CA: all cells obey the same rule Hybrid CA Reversible CA: the global transition function is one-to-one mapping Nonreversible CA Programmable CA: different iteration step using different rules …

  7. Configuration of a CA the state of all cells at time t next time the state of i-th cell at time t the state of i-th cell at time t+1 (1) r is neighborhood radius Take radius as one (Elementary CA) (2)

  8. Rule • Transition rule in 1D CA two neighbors----- (256) (Elementary CA) rule 30 00011110=30 • reversible rule couple (15,85),(51,51),(170,240),(204,204)(Periodic boundary)

  9. Layered Cellular Automata(LCA) • LCA can be viewed as a system,that consist of layers ,and each layer is consists of 1D CA • Transformation function-- • The text is converted into binary form and arranged in layers where each row is considered as a 1D CA with periodic boundary withradius equal to unity. 1D rule are used for encryption on each layer.

  10. A Encryption system based on Layered and Reversible CA(LRCA)

  11. A Encryption system based on Layered and Reversible CA(LRCA) Generation Ruleset 1. Select rules which are reversible (15,85),(51,51),(170,240),(204,204) 2. Index the rules for both encryption and decryption Index:0 1 Map:15---00 51---01 170---10 204---11(encryption) 85---00 51---01 240---10 204---11(decryption) 3. Generate Random series of indexes for example:1101010000010001 1010011011111001 1000110011100011 4. Identify rule set from random series for both encryption and decryption 5. Shifting the rules for each row for both encryption and decryption

  12. A Encryption system based on Layered and Reversible CA(LRCA) • Half Shift Transformation

  13. Security Analysis • Confusion • Diffusion

  14. Security Analysis • Time analysis of LRCA and AES

  15. Encryption based on T-shaped Layered Cellular Automata(TLCA) T-shaped neighbor structure the state of i-th cell at time t: • Elementary CA • Layered CA & T-shaped neighbor structure means the state of k-th layer i-th row j-th column at time t

  16. Rule T38505 rule number called a binary number be composed of the mapping values of all neighboring state from high to low as the rule number of T-shaped cellular automata. 1001011001101001=38505 Encryption based on T-shaped Layered Cellular Automata(TLCA)

  17. Encryption based on T-shaped Layered Cellular Automata(TLCA) • The prove of reversible: For If , so If , that is so

  18. Column Transformation Row Transformation

  19. (Half) Shift Transformation Encryption based on T-shaped Layered Cellular Automata(TLCA)

  20. Encryption based on T-shaped Layered Cellular Automata(TLCA)

  21. Encryption based on T-shaped Layered Cellular Automata(TLCA) • Security Analysis • Avalanche Effect

  22. Security Analysis Avalanche Effect Diffusion Property Encryption based on T-shaped Layered Cellular Automata(TLCA) Number of bits changed in cipher text Number of bits changed in plain text

  23. Thanks!

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